電氣工程及其自動化畢業(yè)設計外文翻譯--一種特殊的預防電壓波動的保護方案

1、;.原文: A SPECIAL PROTECTION SCHEME FOR VOLTAGE STABILITY PREVENTIONTara Alzahawi Student Member, IEEE Mohindar S. Sachdev Life Fellow, IEEE G. Ramakrishna Member, IEEEPower System Research Group University of Saskatchewan Saskatoon, SK S7N 5A9, Canada Abstract Voltage instability is closely related t

2、o the maximum load-ability of a transmission network. The energy flows on the transmission system depend on the network topology, generation and loads, and on the availability of sources that can generate reactive power. One of the methods used for this purpose is the Voltage Instability Predictor (

3、VIP). This relay measures voltages at a substation bus and currents in the circuit connected to the bus. From these measurements, it estimates the Thévenins equivalent of the network feeding the substation and the impedance of the load being supplied from the substation. This paper describes an

4、 extension to the VIP technique in which measurements from adjoining system buses and anticipated change of load are taken into consideration as well. Keywords: Maximum load ability; Voltage instability; VIP algorithm. 1. Introduction Deregulation has forced electric utilities to make better use of

5、the available transmission facilities of their power system. This has resulted in increased power transfers, reduced transmission margins and diminished voltage security margins. To operate a power system with an adequate security margin, it is essential to estimate the maximum permissible loading o

6、f the system using information about the current operation point. The maximum loading of a system is not a fixed quantity but depends on various factors, such as network topology, availability of reactive power reserves and their location etc. Determining the maximum permissible loading, within the

7、voltage stability limit, has become a very important issue in power system operation and planning studies. The conventional P-V or V- Q curves are usually used as a tool for assessing voltage stability and hence for finding the maximum loading at the verge of voltage collapse 1. These curves are gen

8、erated by running a large number of load flow cases using, conventional methods. While such procedures can be automated, they are time-consuming and do not readily provide information useful in gaining insight into the cause of stability problems 2. To overcome the above disadvantages several techni

9、ques have been proposed in the literature, such as bifurication theory 3, energy method 4, eigen value method 5, multiple load flow solutions method 6 etc. Reference 7 proposed a simple method, which does not require off-line simulation and training. The Voltage Indicator Predictor (VIP) method in 7

10、 is based on local measurements (voltage and current) and produces an estimate of the strength / weakness of the transmission system connected to the bus, and compares it with the local demand. The closer the local demand is to the estimated transmission capacity, the more imminent is the voltage in

11、stability. The main disadvantage of this method is in the estimation of the Thévenins equivalent, which is obtained from two measurements at different times. For a more exact estimation, one requires two different load measurements. This paper proposes an algorithm to improve the robustness of

12、the VIP algorithm by including additional measurements from surrounding load buses and also taking into consideration local load changes at neighboring buses. 2. Proposed Methodology The VIP algorithm proposed in this paper uses voltage and current measurements on the load buses and assumes that the

13、 impedance of interconnecting lines (,) are known, as shown in (Figure 1). The current flowing from the generator bus to the load bus is used to estimate Thévenins equivalent for the system in that direction. Similarly the current flowing from other load bus (Figure 2) is used to estimate Th

14、33;venins equivalent from other direction. This results in following equations (Figure 3). Note that the current coming from the second load bus over the transmission line was kept out of estimation in original (VIP) algorithm. 1 2 3 4Where and are currents coming from Thévenin buses no.1 and 2

15、. Equation (1)-(4) can be combined into a matrix form: *5Using the first 2 rows in the system Equations (1)-(4), the voltage on buses number 1 and 2 can be found as shown in Equation (6) below. From Equation (6) we can see that the voltage is a function of impedances. Note that the method assumes th

16、at all Thévenins parameters are constant at the time of estimation. 6Where, and The system equivalent seen from bus no.1 is shown in Figure 3. Figure 4(a) shows the relationship between load admittances ( and ) and voltage at bus no.1. Power delivered to bus no.1 is () and it is a function of (

17、,). 7 Equation 7 is plotted in figure 4 (b) as a landscape and the maximum loading point depends on where the system trajectory goes over the hill. Fig. 1. 3-Bus system connections Fig. 2. 1-Bus model Fig. 3. System equivalent as seen by the proposed VIP relay on bus #1 (2-bus model) (a)Voltage Prof

18、ile (b) Power Profile Fig. 4. Voltage and power profiles for bus #1 2.1. On-Line Tracking of Thévenins Parameters Thévenins parameters are the main factors that decide the maximum loading of the load bus and hence we can detect the voltage collapse. In Figure3, can be expressed by the foll

19、owing equation: 8V and I are directly available from measurements at the local bus. Equation (8) can be expressed in the matrix form as shown below. 9 B= A X 10The unknown parameters can be estimated from the following equation: 11 Note that all of the above quantities are functions of time and are

20、calculated on a sliding window of discrete data samples of finite, preferably short length. There are additional requirements to make the estimation feasible: There must be a significant change in load impedance in the data window of at least two set of Measurements. For small changes in Théven

21、ins parameters within a particular data window, the algorithm can estimate properly but if a sudden large change occurs then the process of estimation is postponed until the next data window comes in. The monitoring device based on the above principle can be used to impose a limit on the loading at

22、each bus, and sheds load when the limit is exceeded. It can also be used to enhance existing voltage controllers. Coordinated control can also be obtained if communication is available. Once we have the time sequence of voltage and current we can estimate unknowns by using parameter estimation algor

23、ithms, such as Ka lm an Filtering approach described 6.stability margin (VSM) due to impedances can be expressed as (); where subscript z denotes the impedance.Therefore we have: 12 The above equation assumes that both load impedances (, ) are decreasing at a steady rate, so the power delivered to b

24、us 1 will increase according to Equation (7). However once it reaches the point of collapse power starts to decrease again.Now assume that both loads are functions of time. The maximum critical loading point is then given by Equation(13): 13Expressing voltage stability margin due to load apparent po

25、wer as ( ), we have: 14Note that both and are normalized quantities and their values decrease as the load increases. At the voltage collapse point, both the margins reduce to zero and the corresponding load is considered as the maximum permissible loading. Fig. 5. VIP algorithm2.2. Voltage Stability

26、 Margins and the Maximum Permissible Loading System reaches the maximum load point when the condition: is satisfied (Figure5).Therefore the voltage stability boundary can be defined by a circle with a radius of the Thévenins impedance. For normal operation the is smaller than (i.e. it is outsid

27、e the circle) and the system operates on the upper part (or the stable region) of a conventional P-V curve 2. However, when exceedsthe system operates on the lower part (or unstable region) of the P-V curve, indicating that voltage collapse has already occurred. At the maximum power point, the load

28、impedance becomes same as the Thévenins (). Therefore, for a given load impedance (), the difference between and can be considered as a safety margin. Hence the voltage as given in an IEEE survey, which described (111) schemes from (17) different countries 8. Fig. 6. Load actions to prevent fro

29、m voltage instability2.3. Advantages of the proposed VIP algorithmBy incorporating the measurements from other load buses (Figure 3), the proposed VIP algorithm achieves a more accurate value of . The on-line tracking of is used to track system changes. The proposed improvements in the VIP algorithm

30、 will result in better control action for power system voltage stability enhancement. The control measures are normally shunt reactor disconnection, shunt capacitor connection, shunt VAR compensation by means of SVCs and synchrouns condensers, starting of gas turbines, low priority load disconnectio

31、n, and shedding of low-priority load 8. Figure 6 shows the most commonly used remedial actions .3. Conclusions An improved Voltage Instability Predictor (VIP) algorithm for improving the voltage stability is proposed in this paper. The previous VIP method 7 used measurements only from the bus where

32、the relay is connected. The new method uses measurements from other load buses as well. The voltage instability margin not only depends on the present state of the system but also on future changes. Therefore, the proposed algorithm uses an on-line tracking Thévenins equivalent for tracking the

33、 system trajectory. The algorithm is simple and easy to implement in a numerical relay. The information obtained by the relay can be used for load shedding activation at the bus or VAR compensation. In addition, the signal may be transmitted to the control centre,where coordinated system-wide contro

34、l action can be undertaken. The algorithm is currently being investigated on an IEEE 30 bus system and results using the improved VIP algorithm will be reported in a future publication. References 1 M.H.Haque, “On line monitoring of maximum permissible loading of a power system within voltage stabil

35、ity limits”, IEE proc. Gener. Transms. Distrib.,Vol. 150, No. 1, PP. 107-112, January, 2003 2 V. Balamourougan, T.S. Sidhu and M.S. Sachdev, “Technique for online prediction of voltage collapse”, IEE Proc.Gener.Transm. Distrib., Vol.151, No. 4, PP. 453-460, July, 2004 3 C.A. Anizares, “On bifurcatio

36、ns voltage collapse and load modeling “IEEE Trans. Power System, Vol. 10, No. 1, PP. 512-522, February, 1995 4 T.J Overbye and S.J Demarco, “Improved Technique for Power System voltage stability assessment using energy methods“, IEEE Trans. Power Syst., Vol. 6, No. 4, PP. 1446-1452, November, 1991 5

37、 P.A Smed Loof. T. Andersson, G. Hill and D.J,”Fast calculation of voltage stability index”, IEEE Trans. Power Syst. Vol. 7, No. 1, PP. 54-64, February, 1992 6 K. Ohtsuka ,” An equivalent of multi- machine power system and its identification for on-line application to decentralized stabilizers”, IEE

38、E Trans. Power Syst., Vol. 4 No. 2, PP. 687-693, May, 1989 7 Khoi Vu, Miroslav M Begovic, Damir Novosel, Murari Mohan Saha, “ Use of local Measurements to estimate voltage stability margin “ IEEE Trans. Power syst. Vol. 14, No. 3, PP. 1029-1035, August, 1999 8 G.Verbic and F. Gubina “Fast voltage-co

39、llapse line protection algorithm based on local phasors”, IEE Proc.Gener.Transm. Distrib., Vol. 150, No. 4, PP. 482-486, July, 2003 譯文：一種特殊的預防電壓波動的保護方案塔拉阿里扎哈維 學生會員,IEEE 摩亨達瑞S.薩凱戴維 院士,IEEE G.羅摩克里希納 會員,IEEE （IEEE:美國電氣和電子工程師協(xié)會）薩斯喀徹溫省薩斯卡通大學的電力系統(tǒng)研究小組,SK S7N 5A9,加拿大摘要電壓的波動與輸電線路的最大負載能力密切相關(guān)。輸電系統(tǒng)中電能的傳輸依賴于輸電線

40、路的拓撲結(jié)構(gòu),發(fā)電和負載,以及無功電源的出處。一種用于分析電壓波動的方法是電壓波動的預測(VIP)。由繼電器測量變電所連接到線路上的電路的電流和電壓。根據(jù)測量結(jié)果,借助戴維南定理估算出輸送到變電所線路和從變電所提供的負載的阻抗。本文描述了一個測量相鄰系統(tǒng)母線并考慮到的負荷預期變化的擴展的VIP技術(shù)。關(guān)鍵詞:最大負載能力;電壓波動;VIP算法。1.簡介寬松的政策迫使發(fā)電企業(yè)要更好地利用電力系統(tǒng)中的輸電。這導致了輸電量的增加,降低了輸電利潤和減小了電壓安全裕度。操作一個有足夠安全裕度的電力系統(tǒng),在系統(tǒng)的使用信息中估算當前操作點的最大允許負載是必要的。一個電力系統(tǒng)的最大負載不是一個固定的值而是取決于

41、各種各樣的因素,比如輸電線路的拓撲、無功電源的出處和他們的位置等等。決定最大允許負載,在電壓穩(wěn)定極限內(nèi),在電力系統(tǒng)運行和規(guī)劃研究中已成為一個非常重要的問題。常見的P-V或V-Q曲線通常當作一個評估電壓穩(wěn)定的依據(jù),進而為在電力系統(tǒng)電壓崩潰端尋找最大負載提供依據(jù)1。這些曲線常規(guī)的方法是在大量負載流運行使用的情況下產(chǎn)生的。雖然這樣的過程已經(jīng)可以自動化,但它們是耗時的,在發(fā)現(xiàn)穩(wěn)定性問題的起因時不易提供一些有用的信息2。為了克服上述缺點的多個方法已經(jīng)在文獻上提到,比如分叉理論3,能量法4、本征值法5,多個負載流解法6等。參考7提出了一個簡單的方法,它不需要離線的模擬和訓練。電壓指標預測方法(VIP)7是

42、在本地測量值(電壓和電流)的基礎上,產(chǎn)生一個連接到母線上估算優(yōu)點和缺點的輸電系統(tǒng),并將它與當?shù)氐男枨髮Ρ?。估算出最接近本地需求的輸電?更為緊迫的是電壓波動。該方法的主要缺點是在戴維南定理的估算,它在不同時刻獲得兩個測量值。對于一個更精確的估值,一般需要兩個不同的負荷測量值。本文提出了一種提高穩(wěn)定性算法的算法,包括周圍負載母線的額外的測量值外也考慮到相鄰總線之間局部的負載變化。2.提出的方法VIP算法在本文中提到在負載母線和互連線( ,)的假設阻抗在已知的情況下使用電壓和電流測量 ,如下所示(圖1)。發(fā)電機負載母線的電流被用來估計戴維南等效的輸電方向。類似于用從其他負載母線(圖2)的電流來估計

43、戴維南等效的其他方向。這個結(jié)果在以下方程式(圖3)。注意在輸電線路上來自第二負載母線的電流被排除在最初的估算(VIP)算法。 1 2 3 4由戴維南定理得來自第一和第二母線的電流和。方程(1)-(4)可以組合為一個矩陣形式: *5使用第一行系統(tǒng)方程(1)-(4)中的2,在母線1和2上的電壓可以發(fā)現(xiàn)如以下方程式(6)所示。從方程式(6)中我們可以看到,電壓是一個阻抗的函數(shù)。請注意這個方法是假定所有戴維南的參數(shù)是常數(shù)時的估算。 6 在 和 中系統(tǒng)等效理解為母線1如圖3所示。圖4(a)顯示了負載通道(y1和y2) 和母線1電壓之間的關(guān)系。電力輸送到母線1是(),它是一個(,).的函數(shù)。 7 方程式7

44、如圖4(b)“形象化”繪制并且最大負載點取決于系統(tǒng)軌跡”超過頂點”。 圖1.3母線系統(tǒng)連接 圖2.1母線模型圖3.系統(tǒng)等效為被提議的VIP轉(zhuǎn)接到母線#1(母線#2模型)(a)電壓分布圖 (b)功率分布圖圖4.母線# 1的電壓和功率分布圖2.1. 即時跟蹤戴維南的參數(shù)戴維南的參數(shù)是決定負載母線最大負載的的主要因素,因此我們可以檢測輸電系統(tǒng)電壓崩潰。在圖3，可以用以下的方程式表示: 8電壓和電流可以從測量本地母線直接得到。方程式(8)可以用矩陣形式表達,如下所示。 9 B= A X 10 未知參數(shù)可以從以下方程式的估算: 11 注意,上述所有數(shù)量的計算是函數(shù)的時間和在滑動窗口的有限的離散數(shù)據(jù)樣本之

45、內(nèi)計算,最好長度是短的。在額外的需求下做出可行的估算:必須有一個顯著的變化，負載阻抗數(shù)據(jù)窗口至少兩組測量值。對于戴維南參數(shù)在一個特殊的數(shù)據(jù)窗口小的變化,該算法可以正確地估算除一個突然大的變化以外，估算的過程推遲到下一個數(shù)據(jù)窗口的到來。這種監(jiān)視裝置基于上述原理可以用來強加限制裝載在每個母線,和流負載超過限制時。它也可以用來加強現(xiàn)有的電壓控制器。協(xié)調(diào)控制同樣可以得到在交流是否空閑的情況下。一旦我們有了時間序列的電壓和電流，我們可以通過使用參數(shù)估算算法估算未知參數(shù),如卡爾曼濾波方法描述6。穩(wěn)定裕度() 由于阻抗可以表示為（）;在下標z表示阻抗。因此我們有: 12上述方程式假設兩個負載阻抗(, )是在一個穩(wěn)定的速度下減少,所以電力送到母線1將根據(jù)方程(7)增加。然而一旦它達到飽和點的時候電力再一次開始減少?，F(xiàn)在,假設兩個負載是時間的函數(shù)。最大的臨界負載點方程式(13)給出: 13 電壓穩(wěn)定裕度表示由于負載視在功率為( ),我們有: 14注意,和兩個都是標準化的定量和隨著負載的增加它們的價值減少。在電力系統(tǒng)電壓崩潰點,同時兩個裕度減少到零和相應的負載被視為最大允許負載。圖5.VIP算法2.2. 電壓穩(wěn)定裕度和最大允許加載系統(tǒng)達到最